Method for obtaining the wheel-rail contact location and its application to the normal problem calculation through CONTACT

[EN] This work presents a robust methodology for calculating inter-penetration areas between railway wheel and rail surfaces, the profiles of which are defined by a series of points. The method allows general three-dimensional displacements of the wheelset to be considered, and its characteristics make it especially suitable for dynamic simulations where the wheel-rail contact is assumed to be flexible. The technique is based on the discretization of the geometries of the surfaces in contact, considering the wheel as a set of truncated cones and the rail as points. By means of this approach, it is possible to reduce the problem to the calculation of the intersections between cones and lines, the solution for which has a closed-form expression. The method has been used in conjunction with the CONTACT algorithm in order to solve the static normal contact problem when the lateral displacement of the wheelset, its yaw angle and the vertical force applied in the wheelset centroid are prescribed. The results consist of smooth functions when the dependent coordinates are represented as a function of the independent ones, lacking the jump discontinuities that are present when a rigid contact model is adopted. Example results are shown and assessed for the normal contact problem for different lateral and yaw positions of the wheelset on the track. This work was supported by the financial contribution of the European Union’s Shift2Rail programme (RUN2Rail project, grant number 777564), the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (projects TRA2013-45596-C2-1-R and TRA2017-84701-R). Baeza González, LM.; Thompson, DJ.; Squicciarini, G.; Denia, FD. (2018). Method for obtaining the wheel-rail contact location and its application to the normal problem calculation through CONTACT. Vehicle System Dynamics. 56(11):1734-1746. https://doi.org/10.1080/00423114.2018.1439178 Garg, V. K., & Dukkipati, R. V. (1984). Wheel–Rail Rolling Contact Theories. Dynamics of Railway Vehicle Systems, 103-134. doi:10.1016/b978-0-12-275950-5.50009-2 Wickens, A. H. (1965). The dynamic stability of railway vehicle wheelsets and bogies having profiled wheels. International Journal of Solids and Structures, 1(3), 319-341. doi:10.1016/0020-7683(65)90037-5 DE PATER, A. D. (1988). The Geometrical Contact between Track and Wheelset. Vehicle System Dynamics, 17(3), 127-140. doi:10.1080/00423118808968898 Yang G. Dynamic analysis of railway wheel